Abstract: The disclosed 2-D and 3-D tomographic resistance imaging method improves tomographic resistance image resolution by adopting an orthogonal basis with the maximum number of elements N to describe the maximum resolution resistivity map ?(r), where this number of elements N is set according to the number of electrodes Q; by defining the orthogonal basis according to any known constraints in the problem, thereby enhancing the resolution where it is needed; by positioning electrodes to be sensitive to these basis functions; and by choosing current I and voltage V contact electrode pairs that maximize signal-to-noise ratio.

Abstract: The disclosed 2-D resistance tomographic imaging method optimizes computation speed for performing electrical impedance tomography using a model-space with a minimal number of orthonormal polynomial basis functions to describe discernable features in the 2-D resistance tomographic image, determining a minimal number of contacts to take fewer measurements than available information based on the number of basis functions, selecting a subset of rows of a matrix of calculated sensitivity coefficients to form a square Jacobian matrix for a linearized forward problem to be solved and inversion of the linear forward problem, and solving an inverse problem based on the square Jacobian matrix by performing at least one iteration of a Newton's method solve.

Abstract: The disclosed 2-D and 3-D tomographic resistance imaging method improves tomographic resistance image resolution by adopting an orthogonal basis with the maximum number of elements N to describe the maximum resolution resistivity map ?(r), where this number of elements N is set according to the number of electrodes Q; by defining the orthogonal basis according to any known constraints in the problem, thereby enhancing the resolution where it is needed; by positioning electrodes to be sensitive to these basis functions; and by choosing current I and voltage V contact electrode pairs that maximize signal-to-noise ratio.